Adaptive Fuzzy Control with Predefined-Time Convergence for High-Order Nonlinear Systems Facing Input Delay and Unmodeled Dynamics

This work addresses the design of a predefined-time adaptive fuzzy control scheme for high-order nonlinear systems with nonstrict-feedback structures, subject to unmodeled dynamics and input time delay. To mitigate the influence of unmodeled dynamics, a predefined-time auxiliary dynamic signal is incorporated into the controller design. Meanwhile, the adverse effects caused by input delay are handled by integrating a Padé approximation with the introduction of an intermediate state variable. Fuzzy logic systems are utilized to approximate the unknown nonlinear terms present in the system dynamics. Based on a recursive backstepping framework and a power-type Lyapunov function formulation, an adaptive fuzzy tracking controller with predefined-time convergence characteristics is constructed. A detailed stability analysis demonstrates that the closed-loop system achieves practical predefined-time convergence, while appropriate selection of design parameters guarantees that the tracking errors remain confined within a small bounded region around the origin. Finally, the effectiveness and advantages of the proposed control strategy are validated through a numerical example and a practical example.